How to Extend Interval Arithmetic So That Inverse and Division Are Always Defined

Authors

Tahea Hossain, University of California, MercedFollow
Jonathan Rivera, Kean UniversityFollow
Yash Sharma, University of California, MercedFollow
Vladik Kreinovich, University of Texas at El PasoFollow

Publication Date

5-2021

Comments

Technical Report: UTEP-CS-20-94b

Published in Reliable Computing, 2021, Vol. 28, pp. 10-23.

Abstract

In many real-life data processing situations, we only know the values of the inputs with interval uncertainty. In such situations, it is necessary to take this interval uncertainty into account when processing data. Most existing methods for dealing with interval uncertainty are based on interval arithmetic, i.e., on the formulas that describe the range of possible values of the result of an arithmetic operation when the inputs are known with interval uncertainty. For most arithmetic operations, this range is also an interval, but for division, the range is sometimes a disjoint union of two semi-infinite intervals. It is therefore desirable to extend the formulas of interval arithmetic to the case when one or both inputs is such a union. The corresponding extension is described in this paper.